Here’s a little puzzle in probability which, in a slightly different form, I gave to my students to work out. I get the papers back tomorrow. To brace myself against that I’m curious what my readers here would make of it.

Possibly you’ve encountered a bit of calendrical folklore which says that Friday the 13ths are more likely than any other day of the week’s 13th. That’s not that there are more Fridays the 13th than all the other days of the week combined, but rather that a Friday the 13th is more likely to happen than a Thursday the 13th, or a Sunday, or what have you. And this is true; one is slightly more likely to see a Friday the 13th than any other specific day of the week being that 13.

And yet … there’s a problem in talking about the probability of any month having a Friday the 13th. Arguably, no month has any probability of holding a Friday the 13th. Consider.

Is there a Friday the 13th this month? For the month of this writing, December 2011, the answer is no; the 13th is a Tuesday; the Fridays are the 2nd, 9th, 16th, 23rd, and 30th. But were this January 2012, the answer would be yes. For February 2012, the answer is no again, as the 13th comes on a Monday. But altogether, every month has a Friday the 13th or it hasn’t. Technically, we might say that a month which definitely has a Friday the 13th has a probability of 1, or 100%; and a month which definitely doesn’t has a probability of 0, or 0%, but we tend to think of those as chances in the same way we think of white or black as colors, mostly when we want to divert an argument into nitpicking over definitions.

Continue reading “How Did Friday The 13th Get A Chance?”

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